Model calculation of core level XPS spectra in early 3d-metal compounds

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Model calculation of core level XPS spectra in early 3d-metal compounds

J. Parlebas

To cite this version:

J. Parlebas. Model calculation of core level XPS spectra in early 3d-metal compounds. Journal de

Physique I, EDP Sciences, 1992, 2 (7), pp.1369-1379. �10.1051/jp1:1992216�. �jpa-00246628�

J.

Phys.

I France 2 (1992) 1369-1379 JULY 1992, PAGE 1369

Classification

Physics

Abstracts

79.60 79.60E

Model calculation of

_core

level XPS spectra in early 3d-metal

compounds

J. C. Parlebas

(*)

IPCMS-GEMME, Universit£ Louis Pasteur, 4 _rue Blaise Pascal, 67070

Strasbourg,

France (Received10 January 1992, revised 23 March 1992,

accepted

I

April1992)

Rdsum4. A l'aide du modble

d'impuret6

d'Anderson _avec

m£lange

de

configurations,

_nous

calculons [es spectres ^{X de la}

photo£mission

de _c«ur (c-XPS) _pour certains

compos£s

isolants du d£but de la sdrie des m6taux de transition (MT). Comme la bande de valence de _ces

compos6s

est

complbtement remplie,

_{on peut} traiter exactement la

rdpulsion

de Coulomb _{U~~ sur} le site du MT ainsi d'ailleurs _que l'interaction _U~~ entre l'dlectron 3d et le trou de _c«ur. L'dtat de base d'un tel

systbme

contenant un cation de

configuration

^d° est ddcrit par un

mdlange

de l'dtat

ionique

purement d° _et des dtats dcrantds h transfert de

charge

^d~L _et d~L^~ oh L _est mis pour un trou dons la bande de valence. Ce modble trbs

simplifid

est par

exemple capable

de

comprendre pourquoi

[es satellites de la

photodmission

de _{c«ur sont} bien

prdsents

dans CaF~ _ou CaO, _comme dons [es

composds

de MT

lagers,

mais absents dans [es

composds

KF. En

plus

de U~~ et U~~, ^[es autres

parambtres pertinents

sont A,

l'dnergie

de transfert de

charge

du m6talloide _vers le m6tal et

l'hybridation correspondante

V (relide _aux intdgrales de transferts

correspondantes).

Aussi, _nous

avons pu obtenir _un bon

ajustement thdorique

du spectre

2p~wXPS,

mesurd dons

TiO~,

et ceci _en

utilisant [es valeurs des

param~tres

foumies par (I) _un calcul de structure de bandes LMTO de

TiO~,

(it) _un calcul des

prdpics

du seuil K(Ti)

d'absorption

dans

TiO~.

Abstract.

Using

_a

configuration-interaction impurity-Anderson

model _we calculate core-hole

X-ray

Photoemission

Spectra

(c-XPS) for _some

early

Transition Metal (TM)

insulating compounds.

Because in these

compounds

the valence

(ligand)

band is

completely

filled, the TM on-site Coulomb

repulsion

_U~~ is treated

exactly,

_as well _as the 3d-core hole interaction U~~. The

ground

state of such _a

ligand-TM

system ^with a

nominally

^d° cation is described _{as a}

mixture of

purely

^d° ionic state, and

charge-transfer

screened d~L _and d~L~ states where L denotes

a hole in the

ligand

band. Our

simplified

model enables us to understand

why

c-XPS satellites are

still present ⁱⁿ

CaF~

_or CaO, like in

light

TM

compounds,

but absent for KF

compounds.

In addition to U~~ and U~~, ^{the other} relevant parameters are the

ligand-to-metal charge-transfer

energy A and the

corresponding hybridization

V (related to the

metal-ligand

transfer

integrals).

Finally quite

a

good

fit to

2p~j~-XPS

of

TiO~

is obtained

by using

the parameter ^{values estimated}

from (I) _a LMTO band _structure calculation of TiO~, and (it) another calculated fit of the K(Ti)

pre-edge absorption

spectrum in

TiO~.

(*) UMR 46 CNRS.

1. Introduction.

Transition-metal

(TM) compounds

have

long

been of great ^{interest in} solid-state

physics,

even more since the

discovery

of

high-temperature superconductivity

in copper oxides. As far

as the electronic structure of

insulating

TM

compounds

is

concemed,

band-structure calculations in which

exchange

and correlation effects _are

replaced by

effective one-electron

potentials happen

to

predict

_{energy gaps,} for

example,

which _{are an} order of

magnitude

Smaller than

experimentally

observed. In order to obtain information _on the correlated nature of the considered 3d-electron

systems,

the

analysis

of the _core level

X-ray photoemission

spectra

(c-XPS)

is

certainly

one of the most useful tolls

([1-3]

and Refs.

therein).

As for the _c- XPS in TM

compounds,

the first successful

attempt

to

give

_a

quantitative interpretation

of the spectra was made

by

van der Laan _et al.

[4]

for copper

dihalides, following

earlier work

by

Larsson and

Braga [5]. Quite generally

it is

possible

to state that the c-XPS of TM

compounds

exhibits not

only

a main line for which the sudden creation of _{a core} hole in the system state is screened _as well _as

possible,

but also satellite

peaks arising

from excitations of the electron system

containing

the _core hole

([4-7]

and Refs.

therein).

In this paper we are interested in the

simplest

mechanism

responsible

for the main-line-versus-satellite-structure in the c-XPS of

early

3d TM

compounds,

which have been less studied than the late _ones.

Recently

and in

good

agreement ^with

experiment, Bocquet

et al.

[8] applied

a

cluster-type configuration

interaction model

([4, 5],

_see also

[9, 10])

to

perform

_a

systematic analysis

of

2p-

XPS for late TM

(Mn,

Fe,

Co, Ni, Cu) compounds, specially

oxides and

sulphides.

It _seems very

tempting

to extend the

configuration-interaction Anderson-type approach (or

_a

simplified version)

to the _case of _some

early

TM

compounds (Ca, Sc, Ti...),

at least _{to test} it

numerically (although

_an additional mechanism has been

proposed by

de Boer et al.

[6]

for

lighter

TM

compounds, specially

in their

vapor-phases [II). Similarly

to the

interpretation

of the c-XPS satellites in

early

rare-earth

insulating compounds [2, 3, II, 12],

the

corresponding

satellites in the

early

TM

insulating compounds

under consideration _are then

viewed, similarly

to the late TM

compounds,

as

originating

from

charge

transfer between 3d and

ligand (anion)

orbitals

(see

Ref.

[13]

for _a

systematic

discussion of

charge

transfer and Mott-

Hubbard types of TM

compounds).

Moreover the satellite

peaks

of _an

insulating

TM

compound

_are often observed _more

clearly

than those of the

corresponding

TM

[14].

Because of

differing screening situations,

the 3d Coulomb interaction used to

interpret

the

K(Ti)

_pre-

edge absorption

in

TiO~ _(U~~

~ 5

eV) [9]

_was found _to be much

larger

than in

early

TM- metallic

systems (U~~

l-2

eV). (As

_an

example,

U~~ ^for an isolated V atom in Cu metal _was found to be about I.I eV

[16]).

The model calculation of the

present

paper is based _on the

filled-band

impurity-type configuration-interaction

Hamiltonian which _can be solved without any

approximation

because of the filled character of the

ligand

band

(LB)

_or valence band

[12].

In this

simple model,

the

physics

of the c-XPS is described in terms of _a few

pertinent parameters, I-e-,

the on-site Coulomb

repulsion

_U~~, the

charge-transfer

_energy

A,

which is _necessary to transfer _one electron from the LB to the metal

orbitals,

the

hybridization

_energy V related to the

metal-ligand

transfer

integrals (which

mix the

previously

considered

types

^of

states),

and the _core hole-d electron Coulomb attraction energy U~~.

The paper is

organized

as follows. In section 2 _we recall _our model formulation of c-XPS in the _case of _a series of

early

TM

insulating compounds nominally

characterized

by

_a 3d°

configuration

in the

ground

state. Then _we

give

some results and

general

discussion relevant to the

early

3d

TM-compounds

considered _as well _as K and

Ca-compounds (Sect. 3).

In

section 4 we try to find _out the best parameters to fit the

experimental

results of

2p~~-XPS

ⁱⁿ

Ti02 17, 17, 18]

in

conjunction

with _a

previous

theoretical fit _to

K(Ti) pre-edge absorption

spectra

[15]

and _a

previous

band structure calculation of

Ti02 l19].

N° 7 CALCULATION OF CORE-XPS SPECTRA IN 3d-METAL COMPOUNDS 1371

2. Model formulation of C~XPS in _some

early

^TM

insulating compounds.

We consider

early

TM

insulating compounds

characterized

by

the

following

band structure

([19]

^for

ex.)

: a

completely

filled

LB, mostly arising

from the anion states and

separated by

an energy gap of _a few eV from the empty ^{conduction d}

bands,

t~~ and

e~ (which

^often

happen

to be

separated

from each other

by

another

gap). Actually

in _our

simplified

formulation _we

only keep

in mind _an electron system

consisting

of _a filled LB and _a

degenerate

3d TM level with the

corresponding

core level

(2s

_or

2p

TM

level). Similarly

to the _case of the 4P La

insulating compounds (La~O~, LaF~ [20]),

the 3d level in the

ground

state of the TM

compound

is assumed _to be well above the

LB,

_so that it is

practically empty;

^this

corresponds

to the

nominally

3d°

configuration. However,

due to

configuration interaction,

we have _to consider _a

strong

^{mixture of 3d° and}

3d~L configurations

where L _{means a}

ligand

hole in the LB

(also

_see the

appreciable hybridization

V found between the LB and the 3d states

by

Ref.

[19]). Actually

_we also consider

3d~L~

in the

ground

state. In the final _state of the

c-XPS,

the 3d level is

pulled

down

by

the _core hole

potential

_U~~ and _a similar

configuration

interaction mixture takes

place

between

c3d~L

_and

c3d~L~

_where

c labels the

core hole. It is

interesting

to notice the

analogy

^of the present ^{situation with what}

happens

ⁱⁿ

copper dihalides

[4]

_or CUO

compounds [21],

for

example,

where

3d~°L

and 3d9

configurations

are

strongly

mixed. The Hamiltonian of _our present system ^{is written} as :

H

=

I _EL(k) at (k, v) aL(k, v)

+

El £ al (v) ad(v)

+ ec

al

_{a~ +}

~, v v

+

) _{£ tat (k,}

_V)

_ad(")

+ h-C-

i

+ k, v

+

udd £ al (v) ad(v) al (v') ad(v') (i al a~) uric £ al (v) ad(v) (2,I)

v>v, _~

where

e~(k), e(

_{and e~ are the}

_energies

of the LB states, 3d level and _core level

respectively

and

at (k, v), at (v)

and

a)

_are the electron creation operators ^{in the}

corresponding

states.

Here k denotes the index of energy level

(k

= I,

N)

in the LB and _v

specifies

both the

spin

and orbital

degeneracies (v

=

I,.. N~). Actually N~

can be taken between 2

(only spin degeneracy)

and 10

(full

d

spin-orbital degeneracy).

However the

spin

and orbital

degeneracies

^for the _core states _are

disregarded

_as well _as the

corresponding spin-orbit coupling (see [21]

for

ex.),

since in the present

simplified

model _we do not try to describe the full

(core-2p) multiplet

structure but

only

_{one component}

_(2p~/~). Similarly

the cubic

crystal

field effect

(see [2 II

for

ex.)

_on the

e(

_{level is}

_ignored

_{since it is not}

a basic

parameter

to obtain

the satellite features. The Hamiltonian used in

equation (2.I)

is based _{on a} broken

translational

symmetry

^for the 3d-states of the TM-ion

(3d-single

site

model).

Such _an

approximation

is

expected

to make _sense if the

dispersional

character of the d-bandwidth is small _as it is

usually

the _case in 3d

insulating compounds.

We

could,

of _course, also break the anion translational symmetry

ending

_up with _a much used cluster calculation

([4, 5, 8, 11,

2

II

and Refs.

therein)

but the LB width is

usually quite large (see [19]

^for

ex.)

and therefore not

negligible. Equation (2.I) simply

treats the 3d-states of the TM-ion _as

impurity

states

(the

core-hole

potential

_U~~

acting

like _an

impurity potential)

in _a lattice formed

by

^{the itinerant}

ligand

states. Let _us recall that in the _case of the present ^filled

LB,

it is easy to derive exact

solutions of the

preceding

_« two-electron _» Hamiltonian

(2.1) [2, 3, 12].

The

ground

state

(g),

where the _core hole is

occupied (a)

_a~

=

I)

is then

expressed

as a linear combination of the

following

basis states _:

1372

N Nd

(d°)

=

fl fl at (k, v) a) (vac) (2.2)

k I v I

d~,

L

(k)

=

fi _{Z at (v) aL(k, v) d°> (2.3)}

Nd

v

d~,

L

(k _i) L(k~))

₌

l~ _£

_~+

(~ )

_~

(~

_~

)

~+

(~ )

~

(~

_~

)j ~0j(~

~

)

/g(/g ~)

^{d I L b I d 2 L I> 2 I- 2}

d d

~~~ ~~

=

~

_~

^(2.4)

/g

(

/g

i ~~ (

"

i) ~L(~

i_>

Vi) ~~

(V2) ~L(~2>

"~

~

) (~

i ~

~2)

d d

~, , ~~

where

(vac)

is the _vacuum state. Also each final state

if)

of the c-XPS is

expressed,

_apart

from the emitted

photoelectron,

as a linear combination of the

following

states :

d°,

_p

)

= a~

d°) (2.

5

)

d~, L(k), p)

=

a~[d~, L(k) (2.6)

d~,

L

(k i)

^L

(k

_{~), p}

= a~

d~,

L

(k i)

L

(k 2) ^{(2. 7)}

An

important quantity

which characterizes _our model system ^{is the}

ligand-to-metal charge

transfer energy A, defined

by

the energy difference between the 3d° and

3d~L configurations

as follows :

A m E

[3d~

L E

[3d°]

=

e( El

,

(2.8)

where

El

is centre of the LB

(hereafter

taken _as the energy

origin).

In _our model _we treat the filled LB _{as a} finite

periodic

system

consisting

of N discrete levels with

equal spacing

_so that

e~(k)

of

equation (2.I)

is _:

e~(k)

₌

El

W/2 ₊

(WIN) (k 1/2)

k

=

I,

N

(2.9)

In the

following

numerical

results,

_{we put} N

=

6,

but this small number is

already

sufficient to

provide

a

good

convergence

[12].

Also

along

the present paper, we take W

= 5.5 eV which

gives

_a

good

order of

magnitude

of the width of _a LB in _a

typical

kind of TM

compounds

we are

considering

:

actually

the

precise

value of 5.5 eV is taken from _a LMTO band structure

calculation

[19]

and _concems the

2p

O band of rutile

Ti02. Finally,

for

simplicity,

_we

put N~

₌ 2, in the

following

numerical

applications.

However the essential features of the

spectrum ^do not

change

much with N

~,

provided

that

N~

V^~ is

kept

constant

[12].

That _means that e.g. V

= 6 eV with

N~

₌ 2 is

essentially equivalent

to V

= 3.46 eV with

N~

₌ 6

(like

t~~) ^{or to V} = 2.68 eV with

N~

=

10

(like

t~~ ⁺

e~).

Disregarding

the interaction of the emitted

photoelectron

with other electrons

(sudden approximation),

the c-XPS is

finally expressed

_as :

F(EB)

=

z if g>

_1~

(no)/ i(E~

+

E~ E~)2

+

r2j _{(2. lo)}

f

where

E~

is the electronic

binding

_energy obtained

by subtracting

the kinetic _{energy e} of the

photoemitted

core electron from the energy w of the incident

photon (E~

= w

e)

_; r labels the

spectral broadening

of _our

empirical

Lorentzian function

(2. lo) arising

from the finite

N° 7 CALCULATION OF CORE-XPS SPECTRA 1N 3d-METAL COMPOUNDS 1373

lifetime of the _core hole _as well _as the

experimental

resolution width. Unless

specified differently,

^r= I eV in the

following.

3. General dhcussion for c-XPS in

early

3d

insulating compounds.

Let _us first remark that in

equation (2. I),

_U~~ and U~~ are not

really independent parameters.

In _our numerical calculation _we take the

parameter

^value U~~ ^{somewhat smaller than}

(or

_at

most

equal to)

_U~~ because the average distance between two d electrons is

usually larger

than the distance between _a d- and _a core-electron

([6, 8]

and Refs.

therein).

For free _atoms, ratios U~~/U~~ ^{have been found} to vary between 0.7 when _c

=

2p

to 0.9 when _c

=

3p [6].

^In

figure

I

we exhibit c-XPS

spectra

^for a range of ratios from U~~/U~~ = 0.666

(Fig. la)

to 0.875

(Fig. lo,

which _seems to be reasonable.

Actually figure

I summarizes _a

qualitative study

of

the effect of

increasing

the

couple _{(U~~, U~~)}

with respect to A fixed. The last parameter ^has

b d~ b

7 I )

<r; m m

E £ _r ^°

~ ~ fl

$ ~

l ~

(a) V (eV) ₌

~ (b) (cl

o

i

o o

ENER6YIe VI ENER6YIeVI ENER6YIeVI

(2,

3)

~~dd'Udc)

(~v) ₌

~~ ~~ (k, 5)

j ^(5,6)

^{~ ~~}

),

^°

'

~fi

^{(I, 8)}

~

W

m

r

W

q~

w

W

I

(

^~j

~

C>

~

~ O

(d) v (ev)

= ~ (e) (r)

3

i

« o ,o °

,o o >o o ,o

ENEReYteV ENEReYte v ENEROYIev

Fig.

I. c-XPS spectra ⁱⁿ 3d°

compounds plotted against binding

_energy for various

hybRdization

strengths ^V ₌ 1, 2,

...,

7 eV and with (U~~, U~~) ₌ (2, 3) eV for (a) _; (3, 4) eV for (b) (4, 5) eV for (c) _; (5, 6)eV for (d) ; (6, 7)eV for (e) _; (7, 8)eV for (f~. The other parameters are A

= 4eV;

N

=

2 r

= I eV.

been chosen to be 4 eV with _a LB width of 5.5

eV,

I-e- _a band gap of 1.25 eV between

e(

and the

highest

state of

LB,

before

considering

_any effect of U~~ or U~~ on

e(.

From

figure

I and

quite generally

it is

possible

to

distinguish

two

regimes

of

parameter

values

[13, 8]

:

(1) (U~~,

U~~) « A like in

figure

la where the satellite is

practically

absent from the spectra

(2) (U~~, U~~)

m A like in

figures

lc,

...,

if,

where the satellite is

clearly visible,

even for small V. For _a

simplified analytical

model restricted to two

configurations

we refer to reference

[4]

_: this model relates the

position

of the satellite and its

intensity

_to A, V and U~~

(but

does not include

U~~).

Veal and Paulikas

[7] reported 2p-XPS

for 2+, 3+ and 4+ cations of

CaF2, SCF~

and

T1F4

fluorides

(see

their

Fig. 7).

For all these

early

3d

insulating compounds

where cationic

configuration

is

nominally

_pure

3d°4s°,

_{satellites are} about lo _to 15 eV

separated

from the main _core line. The situation would be similar for

CaO, Sc20~

and

Ti02

16,

7] (see

next

section for

TiO~).

Satellites

simply replicate

the main

spin-orbit

doublet without

overlapping

it.

Unfortunately

for

V~O~

^{the satellite} structure

(especially

V

(2p~j~))

^is not

easily

observed because of the

superposition

of _a

sharp

O is

peak

at about the _same energy range

[22].

For the calcium

compounds (CaF~, CaO),

the satellite

peaks

are the weakest but still visible.

However in K

2p

^XPS of

potassium

halides like KF

(Fig.

I I of Ref.

[7]),

where the cationic

configuration

also

corresponds

to

3d°4s°,

_no satellite structure _can be discemed and attributed to local

screening

states. In this _case the unfilled 3d _{states are} located too far above the LB

(wide-band-gap material)

_so

that,

even in the final _state of the

2p-XPS,

the 3d levels

are still well above the LB and cannot

participate

to the local

screening

of the _core hole. In

our model calculation

(Fig. 2)

we show

that,

if the transfer energy ^A becomes

larger

and

6 _{(Udd, ~dc)}

"

~3, ~~

~~

al

f

~

$

~ ^°

i

~

_~

o

A

(eV)

=

-

5

o

~

'~_ ~

q ^---

° -io n la m

Et,IERBY'I ei'

Fig.

2. c-XPS spectra ^{in 3d°}

compounds plotted against binding

_energy for various

charge-transfer

energy ^A = 3, 4,

,

9 eV and with (U~~, U~~) = (3, 4) eV (V, N ~) ₌ (5 eV, 2) r

=

I eV.

N° 7 CALCULATION OF CORE-XPS SPECTRA IN 3d-METAL COMPOUNDS 1375

larger,

from 3 to 9

eV,

then the satellite becomes smaller and smaller

(case

of

Ca-compounds)

and

finally disappears (case

of

K-monohalides)

for Ah

(U~~, U~~).

^{It is}

interesting

to underline

that,

on the

opposite

of

K+,

the Ca~+ cation in the final state of the

c-XPS,

shows

low-lying

3d behavior which is

typical

of the cation considered in the whole TM-series of

insulating compounds.

The

important

_common feature is

that,

in the final state, the first

unoccupied

still accessible level is 3d. The

low-binding-energy

c-XPS

peak roughly

corre-

sponds

to a

locally

well screened state 3dl _{and the}

higher binding

_energy satellite to _a

locally poorly

screened _state

3d°.

The fact that K and Ca ions show different but

predictable

satellite

structures

provides

evidence in

support

^{of the 3d}

screening

model of the _core hole. Also the energy

separation

^{between the main and satellite}

peaks (see Eq. (lo)

of Ref.

[4])

is observed to increase in the series

CaF~, SCF~, TiF~ [7]

_or

CaO, SC~O~, TiO~ [6]

_: this would be in

agreement

^with an increase of

hybridization

^V in _our model from Ca to Ti

compounds (Fig. ld,

_{e or}

f~.

4. Case of

2p-XPS

in

(rutile) Ti02.

There has been _a

large

number of

experimental

studies _on 2s _or

2p

Ti c-XPS in

Ti02

compounds (for

_ex.

[7,

17,

18])

_as well _as in related

insulating

oxides like

L14/3Ti~/~04 123]

showing

satellites _on the

high-binding

_energy side _as

generally

discussed in the

preceding

section. In reference

[23], however,

the authors did not

clearly

notice and

interpret

the characteristic satellites.

Furthermore,

_as far _{as we}

know,

there has been _no theoretical attempt to

interpret

and _to fit the c-XPS of

TiO~ quantitatively,

if _we exclude very

)

(fi ^~' Q

~

l

O ^"

~ c>

~>

Z I

.~

r%

,,

r., ~dc ^~~~~

"

8

o

'~

,l'

N ^I'

I

6

a

5

'~

-to o lo m

Ei'iERal'l

_{e ii}

Fig.

3. c-XPS spectra ⁱⁿ 3d°

compounds plotted against binding

_energy for various 3d-core hole interaction Udc " 5,

,

8 eV and with U~~ =

5 eV (V,

N~)

= (6 eV, 2) ; A

=

4 eV r

=

I eV.

1376

preliminary

results

[19]

within the present ^{model where the calculated satellite}

peak happened

to be _too small.

Recently

the

K(Ti)-pre-edge absorption

of

Ti02 lls]

has been

successfully interpreted using

_a somewhat similar Hamiltonian as

equation (2.I) with,

in

particular,

the

following

_parameter values _: A

=

4

eV,

U~~ ₌ ^{5 eV and} _{U~~ =} ^{6 eV. It is}

interesting

to

perform

_a c-XPS calculation

(Fig. 3)

of

Ti02 using

the _same A and U~~

parameter

values _as for

K(Ti)-pre-edge, allowing

_U~~ to vary from 5 eV

(U~~/U~~

₌ ^I to 8 eV

(U~~/U~~

₌

0.625).

Also the width of the LB

(see

Sect.

2)

has been taken from _an LMTO band structure

calculation of

TiO~

in the rutile

phase [19]

and V has been fixed at 6eV with

N~

=

2

(or equivalently

^V

= 3.46 eV with

N~

=

6)

in order _to obtain _a satellite _at about 13.6 from the main line

[7, 17, 18].

From

figure

3 _{we see} that the increase of

strength

of U~~ has _a direct effect _on the increase of

intensity

of the satellite. Next _we

just

test the influence of r

(appearing

in

Eq. (2. lo))

_on the c-XPS

(Fig. 4) (see

Ref.

[8]

for a similar range

of values of

r). Quite obviously

r does _not

change

the spectra, ^but to smaller

r's

correspond

of _{course more}

peaky

spectra.

Finally

_{we report}

(Fig. 5)

the

experimental 2p-

XPS of

TiO~

after

background

subtraction measured

by

reference

[17],

_as well _{as our}

calculated fit with A

= 4 eV, V

=

6 eV, U~~ =

5 eV, U~~ = 7 eV and r

=

0.7 eV. Also for this set of

parameters,

^{table I exhibits the}

weights w(3d~)

of the various 3d~

configuration

contributions with I

=

0, 1,

2. Due _to strong

hybridization V,

the

ground

state

is,

_as

expected,

a

fairly

strong ^{mixture of}

(d°) (~46 ill)

and

[d~L) (~46 ill).

In the final state,

[f~~~~), corresponding

to the most intense

photoemission line,

is also _a strong mixture of

cd~L) (55.0 ill), cd~L~) ^(27.

^I

ill)

but also

cd°) (17.9 ill)

whereas f~~~),

corresponding

to the satellite

peak,

is due to

cd~L~) ^(57.

^I

^ill), cd°) (38.

I

ill)

and

cd~L) (4.8 ill).

Because of

>[>] ©

m

h

o

~ _ii

I

w- rfi

r

(ev)

₌

1.3

~y

j,j .I' I

'

Q

"--, _/~i

~~---' '-

+

0

a

o 0.

'~

-jo R la m

ENERD'iI

_{e v}

Fig.

4. c-XPS spectra ⁱⁿ 3d°

compounds plotted against binding

energy for various

spectral broadenings

r

=

0.7, 0.8,

,

1.3 and with (U~d, U~~) = (5, 7) eV (V, N

d)

_" (6 eV, 2) A

=

4 eV.

N° 7 CALCULATION OF CORE-XPS SPECTRA IN 3d-METAL COMPOUNDS 1377

2p~~~

$

~

~

2Pi

_/~

g

i i~

&90 k60

EREIIGi (eV)

Fig.

5. Dotted line _:

experimental 2p-XPS

of

TiO~

after

background

subtraction (see ^Ref. ill). Full

line calculated

2p~~-XPS

of TiO~ with the

following

parameters:

(U~~,U~~)=(5,7)eV;

(V, N~) = (6 eV, 2) _; A

= 4 eV and r

= 0.7 eV.

Table I.

Weights

_w

of 3d°,

3di _and

3d~

_components

[13], averaged

3d electron number

(n~),

in the

eigenstates g), _[f~~j~)

and

[f~~) E~

and A _are the

position

and

amplitude of [f~~i~)

^and _f~~~) ^the

corresponding

_energy

separation

between satellite and main line is here

13.6 eV. The parameter values _are the

following _{(U~~, U~~)}

=

(5,7)

eV

(V, N~)

=

(6 eV, 2)

_; A

= 4 eV and r

=

0.7 eV.

w(3d°) w(3di) w(3d~) (n~) EB (eV)

A

(g)

_{0.461 0.461 0.078 0.617}

[f~~;~)

^{0,179 0.550 0.271 1.092} 5.922 0.868

f~~~) 0.381 0.048 0.571 1.190 ₊ 7.666 0.084

the _core hole effect the contribution of the 3d~

configuration happens

to be

quite significant

in the final _state

(it

is

only

7.8 ill in the

ground state).

It would _even be

interesting

to extend the

present ^model to test if the 3d3 contribution is

negligibly

small.

Finally

let _us

give

the

following

comment _on the value of A.

According

to the Hartree-Fock

approximation

of

equation (2.I)

in the initial state, A should be

replaced by

A~~~ = A ₊

(n~) _U~~,

which takes the electronic correlations into account, at least in _{a mean} field

approximation,

and

gives

about 7.I eV

(with (n~) 0.62).

This value of _A~~~, I.e.

e]~(

^{counted from the} centre of the

LB,

is in

rough

agreement ^{with the actual}

position

of the t2g ^{band in reference}

[19].

5. Conclusion.

In this paper we

essentially

calculated c-XPS

resulting

from the creation of _{a core} hole _c within the filled band

impurity

Anderson model. Our

simplified

calculations _{seem to}

explain

well the spectra ^of a series of

early

TM

insulating compounds,

characterized

by

_a

nominally

1378

3d°

configuration

in the

ground

_state,

including

those

compounds

which involve _a pre- transitional element such _as K _or Ca.

Moreover,

without

including

_any additional mechanism

[6],

_our model is able to fit

reasonably

well the

2p~~-XPS

of

TiO~ using

values of

parameters

in accord with _a

previous

band structure calculation

[19]

and with _a recent calculated

K(Ti)

pre-edge absorption _spectrum [15].

From the value of A, U~~ ^and U~~ we conclude that

TiO~

resembles the late TM

compounds

as far _as the

interpretation

of the c-XPS spectra ^is concemed _:

TiO~ belongs

_to the

charge

transfer

regime [13, 8],

I.e. A _«

(U~~, U~~). Probably

Sc and Ca

insulating compounds

are at the border line of this

regime.

The

present

model calculation is restricted to

nominally

_pure

^3d° configuration

in the

ground

state like T14+ insulators. A very

interesting

extension would be to consider for

example

_a

nominally

3d°.5 metallic system, ^like

LiTi~04,

and to treat it _{as a} mixed valence system

(T13+, T14+)

in the

ground

_state, which remains _out of the scope of _a

single

Ti site model. One way to

improve

the present

formulation, by including

multi Ti site

interactions,

would then be to extend

equation (2.I)

to a

periodic

Anderson model

[3],

I.e. the _two

(hybridized)

band Hubbard Hamiltonian. This would be

adequate

to describe the evolution of c-XPS

during

the

insulating-metallic

transition when

going

from

Li~/~Ti~/~O~

to

LiTi~O~

_or

TiO~

to

T120~

_or also

V20~

to

VO~.

This

study

is _now in progress.

Acknowledgments.

The author would like to thank Profs. A.Kotani and

A.Kuzemsky,

Drs. A.

Khan,

E.

Beaurepaire

and J. P.

Kappler

for collaboration and discussion. He would also like _to express his thanks to the referees for

pertinent

and valuable remarks and comments.

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N° 7 CALCtIiATION OF CORE-XPS SPECTRA IN 3d-METAL COMPOUNDS 1379

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